Question

solve \\((t - 3)^2 = 6\\). the arrow is at a height of \\(48\text{ ft}\\) after approximately \\(\text{s}\\) and after \\(\text{s}\\).

Explanation:

⚡ Using what you learned: factoring and solving quadratic equations

Step 1: Take the square root of both sides

$$ (t - 3)^2 = 6 $$

$$ t - 3 = \pm\sqrt{6} $$

Step 2: Solve for \( t \)

$$ t = 3 \pm \sqrt{6} $$

Step 3: Calculate approximate decimal values

Using \(\sqrt{6} \approx 2.45\):

$$ t_1 \approx 3 - 2.45 = 0.55 $$

$$ t_2 \approx 3 + 2.45 = 5.45 $$

Rounding to the nearest tenth:

$$ t_1 \approx 0.6 $$

$$ t_2 \approx 5.4 $$

Answer:

The arrow is at a height of 48 ft after approximately 0.6 s and after 5.4 s.